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<h1 class="reftitle">outerApprox</h1>
<h2>Purpose</h2>
<p>Computes outer bounding box of the convex set.</p>
<h2>Syntax</h2>
<pre class="synopsis">B = outerApprox(S)</pre>
<pre class="synopsis">B = S.outerApprox</pre>
<h2>Description</h2>
<p></p>
	  Compute the smallest axis-aligned hypercube that contains this set. The lower and upper bounds
        of the hypercube are stored under <tt>Internal</tt> property, i.e. <tt>Internal.lb</tt> for lower
        bound and <tt>Internal.ub</tt> for upper bound.
	<h2>Input Arguments</h2>
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<td><tt>S</tt></td>
<td>
<p></p>Any set derived from <tt>ConvexSet</tt> class, e.g. <tt>YSet</tt> or <tt>Polyhedron</tt>.<p>
	    		Class: <tt>ConvexSet</tt></p>
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<h2>Output Arguments</h2>
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<td><tt>B</tt></td>
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<p></p>Bounding box <img src="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox1.png"> described as <tt>Polyhedron</tt> in H-representation.<p>
	    		Class: <tt>Polyhedron</tt></p>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Describe circle in 2D using YALMIP<pre class="programlisting">x = sdpvar(2,1);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">F = [x'*x&lt;=1];</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S = YSet(x,F); </pre>
<pre class="programlisting"></pre> The bounding box for the circle is a cube with diameter 1. <pre class="programlisting"> B = S.outerApprox </pre>
<pre class="programlisting">Polyhedron in R^2 with representations:
    H-rep (redundant)   : Inequalities   4 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
</pre> Plot the sets <pre class="programlisting"> S.plot; hold on; B.plot </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox_img_1.png" width="60%"></p>
<h3>Example 
				2</h3>We have a lower dimensional polyhedron in 3D.<pre class="programlisting"> P = Polyhedron('A',randn(9,3),'b',ones(9,1),'Ae', randn(1,3),'be',0.5);</pre>
<pre class="programlisting"></pre> Compute the bounding box<pre class="programlisting"> B = P.outerApprox; </pre>
<pre class="programlisting"></pre> Plot the sets such that the outer approximation is wired. <pre class="programlisting"> P.plot; hold on; B.plot('wire',true,'LineWidth',3) </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox_img_2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/outerapprox_img_2.png" width="60%"></p>
<h2>See Also</h2>
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<br><p>©  <b>2010-2013</b>     Colin Neil Jones: EPF Lausanne,    <a href="mailto:colin.jones@epfl.ch">colin.jones@epfl.ch</a></p>
<p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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